Method and apparatus for reading data from flash memory

ABSTRACT

Methods and apparatus are disclosed, such as those involving a flash memory device that includes an array of memory cells. One such method includes detecting values of charges stored in selected memory cells in the memory cell array. The method also includes processing the detected values in accordance with a Viterbi algorithm so as to determine data stored in the selected memory cells. In one embodiment, the flash memory cell array includes word lines and bit lines. Detecting the values of charges includes detecting values of charges stored in a selected row of memory cells by selecting one of the word lines. The Viterbi algorithm provides correct data where inter-signal interference between the cells affects the accuracy of read data. For example, the Viterbi algorithm can be used to supplement error correction codes (ECC).

BACKGROUND

1. Field of the Invention

Embodiments of the invention relate to memory devices, and more particularly, in one or more embodiments, to flash memory devices.

2. Description of the Related Art

Flash memory devices are non-volatile memory devices which store information on a semiconductor in a way that needs no power to maintain the information stored therein. Flash memory devices typically include an array of memory cells in a matrix form having columns and rows. Each memory cell includes a charge storage node, such as a floating gate transistor formed on a semiconductor substrate. The cells are arranged to form strings such that the source of the transistor of each cell is coupled to the drain of the transistor of a neighboring cell in each string. The memory cell array includes sense lines (often referred to as bit lines), each of which connects to a column of cells in the memory cell array. The memory cell array also includes select lines (often referred to as word lines), extending perpendicular to the bit lines and parallel to one another. Each of the word lines connects to the control gates of the transistors in a row of cells in the memory cell array.

As the geometry of a flash memory is reduced, distances between cells in the memory cell array are also reduced. These reduced distances may incur inter-signal interference (ISI) between neighboring memory cells. The term “inter-signal interference” refers to electromagnetic effect of electrons trapped in the charge storage node of one memory cell on a neighboring memory cell. The inter-signal interference may affect the operation of a flash memory device. Therefore, there is a need for an error-correcting logic or algorithm for flash memory devices with a reduced size.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments will be better understood from the Detailed Description of Embodiments and from the appended drawings, which are meant to illustrate and not to limit the embodiments, and wherein:

FIG. 1 is a schematic diagram of a memory cell array of a NAND flash memory device according to one embodiment;

FIG. 2 is a schematic cross-section of the NAND flash memory device of FIG. 1 according to one embodiment;

FIG. 3A is a diagram illustrating written data bits and corresponding numbers of trapped electrons in an ideal NAND flash memory array without inter-signal interference;

FIG. 3B is a diagram illustrating data bits read from a NAND flash memory array with inter-signal interference;

FIG. 4 is a schematic block diagram illustrating a NAND flash memory array having inter-signal interference;

FIG. 5A is a diagram illustrating an example of a write operation on a NAND flash memory;

FIG. 5B is a diagram illustrating an example of a read operation on a NAND flash memory;

FIGS. 6A-6J illustrate a method of correcting data read from a NAND flash memory array using a Viterbi algorithm according to one embodiment; and

FIG. 7 illustrates a method of correcting data read from a NAND flash memory array using a Viterbi algorithm according to another embodiment.

DETAILED DESCRIPTION OF EMBODIMENTS

As described above, as the geometry of a flash memory device is reduced, distances between cells in the memory device are also reduced. In such a flash memory device, inter-signal interference may affect the operation (particularly, data read operation) of the flash memory device. Therefore, there is a need for an error-correcting logic or algorithm for flash memory devices.

In one embodiment, a flash memory device is provided with an error-correcting logic or algorithm for data read operations, based on a Viterbi algorithm or its variant. Raw data read from a flash memory device is processed using the Viterbi algorithm. A graph called a trellis may be constructed to include all possible combinations of data states that can be stored in a row of cells in the flash memory. A data path with a minimum error is determined using a Viterbi algorithm, thereby providing correct data.

FIG. 1 illustrates a NAND flash memory array according to one embodiment. The illustrated flash memory array includes first to M-th bit lines BL0-BLM and first to N-th word lines WL0-WLN. The bit lines BL0-BLM extend parallel to one another in a column direction. The word lines WL0-WLN extend parallel to one another in a row direction. The NAND flash memory array also includes select transistors 120 a, 120 b used for selecting a bit line.

Each bit line includes a string of floating gate transistors coupled in series source to drain. For example, the second bit line BL1 includes floating gate transistors 110 connected in series. The control gates of floating gate transistors 110 of cells in the same row are coupled to the same word line. Each of the floating gate transistors 110 forms a memory cell that stores a charge (or a lack of charge), wherein the amount of stored charge can be used to represent, for example, one or more states, and wherein the one or more states can represent one or more digits (e.g., bits) of data. The memory cell can be either a single-level cell (SLC) or a multi-level cell (MLC). In one embodiment, the amounts of charge stored in the floating gate transistors 110 may be detected by sensing currents flowing through the floating gate transistors 110. In another embodiment, the amounts of charge stored in the floating gate transistors 110 may be detected by sensing the threshold voltage values of the floating gate transistors 110.

FIG. 2 illustrates a cross-section of the floating gate transistors 110 in the second bit line BL1. The floating gate transistors 110 are formed on a substrate 201. Each of the floating gate transistors 110 includes a source region 210 (which is a drain region for a neighboring transistor), a drain region 212 (which is a source region for a neighboring transistor), a doped channel region 214, a first dielectric (e.g., a tunnel oxide) 216, a floating gate 218, a second dielectric (e.g., a gate oxide, wherein the tunnel and gate oxide can be formed of the same or different material) 220, and a control gate 222. The tunnel oxide 216 is formed on the channel region 214 to insulate the floating gate 218 from the channel region 214. The gate dielectric 220 physically and electrically separates the floating gate 218 from the control gate 222. The control gate 222 is coupled to an appropriate word line, e.g., word line WL1. Electrons can be trapped on the floating gate 218 and be used to store data.

Referring to FIG. 3A, memory cells include a certain number (including zero) of electrons trapped therein, depending on the stored data. For the sake of illustration, suppose that a floating gate transistor has no trapped electrons in its floating gate to store “1” (can be vice versa). Also suppose that a floating gate transistor forming a memory cell can trap 8 electrons in its floating gate to store “0.” The numbers of electrons herein are arbitrary numbers for the sake of explanation, and a skilled artisan will appreciate that the numbers of electrons vary widely depending on the design of the memory cell array.

Ideally, when a stored data bit is “1,” a current sensed to detect the state of the memory cell would indicate that the cell has no trapped electrons (i.e., the presence of a current flow). On the other hand, when a stored data bit is “0,” a current sensed to detect the state of the memory cell would indicate that the cell has 8 trapped electrons (i.e., the absence of a current flow).

A current sensed to detect the state of the memory cell may indicate that the number of trapped electrons is in a continuous range rather than either 0 or 8. Therefore, a threshold value for a sensed current is set to determine whether the memory cell has data of either “1” or “0” (or more states for multi-level cells). In the illustrated example, the threshold value can be 4, i.e., if there are 4 or more trapped electrons, the stored data is “0”; if there are less than 4 trapped electrons, the stored data is “1.” For example, in FIG. 3B, the trapped electrons are 0, 11, 5, and 0 in a row of memory cells. The trapped electrons indicate that the stored data b₀, b₁, b₂, b₃ are 1, 0, 0, 1.

As the geometry of the NAND flash memory is reduced, distances between cells in the memory cell array are also reduced. These reduced distances may incur inter-signal interference (ISI) between neighboring memory cells. Referring to FIG. 4, a NAND flash memory includes a memory cell array 400. In the illustrated embodiment, a memory cell 410 may experience inter-signal interference from neighboring memory cells 421-424 in the same row and/or in the same column.

This inter-signal interference may affect read operations of the NAND flash memory. For example, if one or more of the adjacent memory cells 421-424 has 8 electrons trapped therein, the memory cell 410 may appear when sensed as if it has 2 more electrons than it actually has. For example, the memory cell 410 may appear when sensed as if it has 2 electrons even if it actually has no electrons, or 10 electrons even if it actually has 8 electrons.

Because of the inter-signal interference, when a number of electrons is close to a threshold value, the data can be read inaccurately. For example, when the number of actually trapped electrons is 3, the number sensed may correspond to 5 when there is inter-signal interference. For example, referring back to FIG. 3B, the third bit b2 may be in fact 0 because the read number of electrons (“5”) may be a result of inter-signal interference. In the illustrated example, the threshold is “4.” The cell storing the third bit b2 may appear as if it has 5 electrons even though it actually has 3 electrons.

Referring to FIGS. 5A-5B and 6A-6J, a method of confirming/correcting data read from a NAND flash memory array according to one embodiment will now be described in detail. In the illustrated embodiment, a Viterbi algorithm is used for confirming/correcting data read from a NAND flash memory. A Viterbi algorithm is an algorithm for finding the most likely sequence of hidden states, which is called the Viterbi path. Given observed patterns of trapped electrons in a row of memory cells, the Viterbi algorithm is used to determine the most likely states of the memory cells in the row in consideration of inter-signal interference.

In the illustrated embodiment, it is assumed that one cell in a row exerts inter-signal interference only on a cell immediately next to the one cell in the same row (e.g., in the left-to-right direction). However, a skilled artisan will appreciate that the Viterbi algorithm can be extended to other neighboring cells around any given cell.

Suppose that a cell storing logic “1” has 0 electrons in its floating gate and that a cell storing logic “0” has 8 electrons in its floating gate. A particular cell is not affected by a neighboring cell immediately next to the particular cell in the same row on the left side, if the neighboring cell stores “1” (e.g., no trapped electrons). If, however, the neighboring cell stores “0” (e.g., 8 trapped electrons), the particular cell may experience inter-signal interference from the neighboring cell as if it has two more electrons in addition to its own trapped electrons.

Referring to FIG. 5A, for the purpose of illustration, suppose that data written on four cells b1-b4 in row 1 are 1, 0, 1, 1. Referring to FIG. 5B, now suppose that sensed information from the cells b1-b4 indicate that the cells b1-b4 store 0, 11, 5, and 0 electrons, respectively. These numbers of electrons for cells b1-b4 will be reused in the example of FIGS. 6A-6J as the read number. If the threshold value is 4 electrons (if there are 4 or more electrons, the stored data is 0; if there are less than 4 electrons, the stored data is 1), the read data can be translated to 1, 0, 0, 1 which is not identical to the written data, 1, 0, 1, 1.

Referring to FIGS. 6A-6J, a Viterbi algorithm is used to confirm/correct the data read from the row of cells b1-b4. In the Viterbi algorithm, a path of minimum error along a trellis is determined to indicate the correct data. Errors associated with data states along the trellis are determined by a deviation D which is represented by Equation 1:

D=(RE−PE)²  (1)

In Equation 1, RE is a read number of electrons, and PE is a possible number of electrons in a next state along the trellis. The RE data used will be 0, 11, 5, and 0. As a path is taken along the trellis, the error is accumulated. An accumulated error Ei is represented by Equation 2:

$\begin{matrix} {{Ei} = {\sum\limits^{i}{Di}}} & (2) \end{matrix}$

In Equation 2, Ei is an accumulated error at each destination state, and Di is a deviation at the destination state. The alternative paths (from 0 or 1) leading to each state (1 or 0) are compared to one another. Only the path with a minimum error is selected at each destination state. This process is repeated until the paths to all the given states are determined. The selected paths serve to indicate the correct data stored in the memory cells.

In FIGS. 6A-6J, the upper row represents states where a data bit stored in a memory cell is 1 whereas the lower row represents states where a data bit stored in a memory cell is 0. Each number adjacent to an arrow in FIGS. 6A-6J is a number of electrons that can be expected to be sensed in the next cell. The numbers of electrons herein are arbitrary for the sake of explanation, and a skilled artisan will appreciate that the numbers of electrons vary widely depending on the design of the memory cell array and sensitivity of cells and/or sense circuits.

The numbers had prior states all “1,” i.e., the initial condition is that the accumulated error is 0. In FIG. 6A, the state of an initial cell b0 can be either at 1 or at 0. For the path where the initial cell b0 is at 1 and a first cell b1 is at 1, the possible number of electrons (PE) stored in the first cell b1 is 0 because there is no inter-signal interference by the initial cell b0 on the first cell b1. In the example, the read number of electrons (RE) is 0 for b1, and an accumulated error E1 a associated with this path (1 to 1) is (RE−PE)²=(0−0)²=0.

For the path where the initial cell b0 is at 1 and the first cell b1 is at 0 (path 1 to 0), the possible number of electrons in the first cell b1 is 8 because the first cell b1 would have 8 electrons without inter-signal interference by the initial cell b0. Thus, an accumulated error E1 c associated with this path (1 to 0) is (0−8)²=64.

On the other hand, for the path where the initial cell b0 is at 0 and the first cell b1 is at 1, the possible number of electrons sensed is 2 because the first cell b1 would store no electrons therein but experience inter-signal interference (2 electrons) from the initial cell b0. Thus, an accumulated error E1 b associated with this path (0 to 1) is (0−2)²=4.

For the path where the initial cell b0 is at 0 and the first cell b1 is at 0, the first cell b1 would store 8 electrons with inter-signal interference (2 electrons) from the initial cell b0, thus acting as if it has 10 electrons. Thus, an accumulated error E1 d associated with this path (0 to 0) is (0−10)²=100.

Based on the amounts of the accumulated errors, one of the paths leading to each of the destination states (0 or 1) is eliminated, as indicated by being crossed out. In FIG. 6B, for destination state 1, the arrow from 0 to 1 has been crossed out because the accumulated error E1 b associated with this path from 0 to 1 is greater than the accumulated error E1 a associated with the other path from 1 to 1. Similarly, the arrow from 0 to 0 has been crossed out because the accumulated error E1 d is greater than the accumulated error E1 c. The accumulated errors are drawn inside the circles indicating the destination states.

In FIG. 6C, the read number of electrons (RE) for the second cell b2 in the illustrated example is 11. The first cell b1 can be either at 1 or at 0. For the computation of accumulated error, the first cell b1 has 0 for state 1 and 64 for state 0. For the path where the first cell b1 is at 1 and a second cell b2 is at 1, the possible number of electrons sensed for the second cell b2 would be 0 electrons because the second cell b2 has no stored electron therein with no inter-signal interference from the first cell b1. Thus, a deviation D is (11−0)²=121. For the path where the first cell b1 is at 1 and the second cell b2 is at 0, a deviation D is (11−8)²=9. The accumulated errors E2 a, E2 c are 121 and 9, respectively.

On the other hand, for the path where the first cell b1 is at 0, the accumulated error starts at 64. For the path to destination state 1 of the second cell b2, a deviation D is (11−2)²=81, and an accumulated error E2 b is 145 because the accumulated error of the preceding path adds to the deviation of the current path. For the path where the first cell b1 is at 0 and the second cell b2 is at 0, a deviation D is (11−10)²=1, and an accumulated error E2 d is 65.

Again, based on the amounts of the accumulated errors, one of the paths leading to each of the destination states (0 or 1) is eliminated, as indicated by being crossed out. In FIG. 6D, the arrow from 0 to 1 has been crossed out because the accumulated error E2 b of 145 associated with the path from 0 to 1 is greater than the accumulated error E2 a associated with the other path from 1 to 1. Similarly, the arrow from 0 to 0 has been crossed out because the accumulated error E2 d associated with the path from 0 to 0 is greater than the accumulated error E2 c associated with the other path from 1 to 0.

In FIG. 6E, the read number of electrons (RE) for the third cell b3 is 5 for the illustrated example. The state of the second cell b2 can be either at 1 or at 0. For the path where the second cell b2 is at 1 and a third cell b3 is at 1, a deviation D is (5−0)²=25, and an accumulated error E3 a is 146. For the path where the second cell b2 is at 1 and the third cell b3 is at 0, a deviation D is (5−8)²=9, and an accumulated error E3 c is 130.

On the other hand, for the path where the second cell b2 is at 0, and the third cell b3 is at 1, a deviation D is (5−2)²=9, and an accumulated error E3 b is 18. For the path where the second cell b2 is at 0 and the third cell b3 is at 0, a deviation D is (5−10)²=25, and an accumulated error E3 d is 34.

Again, based on the amounts of the accumulated errors, one of the paths leading to each state (0 or 1) is eliminated, e.g., crossed out. In FIG. 6F, the arrow from 1 to 1 has been crossed out because the accumulated error E3 a is greater than the accumulated error E3 b for the path from 0 to 1. Similarly, the arrow from 1 to 0 has been eliminated because the accumulated error E3 c for the path from 1 to 0 is greater than the accumulated error E3 d for the path from 0 to 0.

In FIG. 6G, the read number of electrons (RE) for the fourth cell b4 is 0 for the illustrated example. The state of the third cell b3 can be either at 1 or at 0. For the path where the third cell b3 is at 1 and a fourth cell b4 is at 1, a deviation D is (0−0)²=0, and an accumulated error E4 a is 18. For the path where the third cell b3 is at 1 and the fourth cell b4 is at 0, a deviation D is (0−8)²=64, and an accumulated error E4 c is 82.

On the other hand, for the path where the third cell b3 is at 0 and the fourth cell b4 is at 1, a deviation D is (0−2)²=4, and an accumulated error E4 b is 38. For the path where the third cell b3 is at 0 and the fourth cell b4 is at 0, a deviation D is (0−10)²=100, and an accumulated error E4 d is 134.

Again, based on the amounts of the accumulated errors, one of the paths leading to each of the states (0 or 1) is eliminated. In FIG. 6H, the arrow from 0 to 1 has been crossed out because the accumulated error E4 b for the path from 0 to 1 is greater than the accumulated error E4 a for the path from 1 to 1. Similarly, the arrow from 0 to 0 has been crossed out because the accumulated error E4 d for the path from 0 to 0 is greater than the accumulated error E4 c for the path from 1 to 0.

FIG. 6I illustrates a resulting path including the arrows remaining after the completion of the process described above. Now, errors at possible states for the fourth cell b4 are compared to each other. In the illustrated example, for the destination state “1,” the accumulated error is 18. For the destination state “0,” the accumulated error is 82. The smaller the error is, the more likely the cell has the state. Thus, it is more likely that the fourth cell b4 stores “1.” Then, a path is taken backward from state “1” of the fourth cell b4. Thus, the third cell b3 likely stores 1. The second cell b2 likely stores 0. In addition, the first cell b1 likely stores 1. Thus, the correct data is 1, 0, 1, 1, which is identical to the written data, as shown in FIG. 6J.

In another embodiment, inter-signal interference on a particular cell by two or more neighboring cells may be taken into account in determining correct data using a Viterbi algorithm. For example, inter-signal interference on a particular cell by a neighboring cell in a row immediately above the particular cell can be taken into account in processing raw data using the Viterbi algorithm. Referring to FIG. 7, a delta (Δ) is added to a possible number of electrons in each state. The delta (Δ) represents the inter-signal interference from a neighboring cell in a row immediately above a particular cell. In one embodiment in which inter-signal interference between cells in the same row amounts to 2 electrons, the delta may be in a range between about 0 and about 2. The detailed process of the Viterbi algorithm can be as described earlier with reference to FIG. 6A-6J except that the delta is added to the possible number of electrons in each state.

In the embodiments described above, the cells are configured to store one of two states, i.e., single level cells. In other embodiments, multi-level cells can be used to store multi-levels, e.g., more than two states. In such embodiments, a Viterbi algorithm can also be adapted to confirm or correct data read from the cells.

As described above, a Viterbi algorithm may be performed on every row of data bits read during read operations. In certain embodiments, a Viterbi algorithm may be performed only on a selected block of data which is suspected to have at least one error. In other embodiments, a Viterbi algorithm may be performed only on a selected block of data which includes a value close to a threshold value (e.g., 5 electrons where the threshold is 4 electrons) or in response to an uncorrectable error to supplement error correction codes (ECC). A skilled artisan will appreciate that various alternative ways of applying a Viterbi algorithm to NAND flash read operations are also possible. In addition, a skilled artisan will appreciate that any modified Viterbi algorithm or a similar algorithm can also be adapted for flash read operations.

In the embodiments described above, a Viterbi algorithm can be performed by any suitable processor or circuit within the NAND flash memory device. In other embodiments, an external processor or circuit may be provided to perform the Viterbi algorithm. A skilled artisan will appreciate that any suitable configuration of processors circuits can be used for performing the Viterbi algorithm as described above.

A flash memory device according to the embodiments described above can be incorporated in various electronic devices. Examples of the electronic devices can include, but are not limited to, consumer electronic products, electronic circuits, electronic circuit components, parts of the consumer electronic products, electronic test equipments, etc. Examples of the consumer electronic products include, but are not limited to, a mobile phone, a telephone, a television, a computer monitor, a computer, a hand-held computer, a personal digital assistant (PDA), a microwave, a refrigerator, a stereo system, a cassette recorder or player, a DVD player, a CD player, a VCR, an MP3 player, a radio, a camcorder, an optical camera, a digital camera, a washer, a dryer, a washer/dryer, a copier, a facsimile machine, a scanner, a multi functional peripheral device, a wrist watch, a clock, etc. Further, the electronic device can include unfinished products.

One embodiment is a method of retrieving data from a memory cell. The method includes determining values associated with data stored by selected memory cells in an array of memory cells; and processing the determined values in accordance with a Viterbi algorithm so as to determine the data stored in the selected memory cells.

Another embodiment is a method of retrieving data from a memory cell. The method includes sensing an electrical condition of a first memory cell within an array of memory cells; and determining a logical state for the first memory cell based at least in part on the electrical condition and an electrical condition and/or logical state associated with at least one memory cell of the array adjacent to the first memory cell.

Yet another embodiment is an apparatus including an array of memory cells. Each of the memory cells is configured to store charges indicative of a data digit. The apparatus also includes a sense circuit configured to detect values of the charges stored in selected ones of the memory cells. The apparatus is configured to process the detected values in accordance with a Viterbi algorithm.

Although this invention has been described in terms of certain embodiments, other embodiments that are apparent to those of ordinary skill in the art, including embodiments that do not provide all of the features and advantages set forth herein, are also within the scope of this invention. Moreover, the various embodiments described above can be combined to provide further embodiments. In addition, certain features shown in the context of one embodiment can be incorporated into other embodiments as well. Accordingly, the scope of the present invention is defined only by reference to the appended claims. 

1. A method of retrieving data from a memory cell, the method comprising: determining values associated with data stored by selected memory cells in an array of memory cells; and processing the determined values in accordance with a Viterbi algorithm so as to determine the data stored in the selected memory cells.
 2. The method of claim 1, wherein each of the memory cells includes a floating gate transistor, wherein determining the values comprises sensing currents flowing through the floating gate transistors or sensing the threshold voltage values of the floating gate transistors.
 3. The method of claim 1, wherein processing the determined values comprises: determining errors associated with paths leading to each possible state of a selected memory cell at least partially based on the determined values and inter-signal interference on the selected memory cell; and selecting one of the paths leading to each possible state at least partially based on an accumulation of the determined errors such that the selected one of the paths has a minimum accumulated error.
 4. The method of claim 3, wherein the memory cells are arranged in columns and rows, wherein processing the determined values comprises sequentially repeating determining the errors and selecting one of the paths for each of a selected row of memory cells.
 5. The method of claim 4, wherein processing the determined values further comprises: selecting a state of the last memory cell in the selected row of memory cells at least partially based on errors associated with paths leading to possible states of the last memory cell; and selecting a state of each of the other memory cells in the selected row of memory cells backward from the selected state of the last memory cell, using the selected paths having a minimum accumulated error, thereby determining the data stored in the memory cells.
 6. The method of claim 3, wherein the inter-signal interference comprises inter-signal interference from one or more memory cells adjacent to the selected memory cell.
 7. The method of claim 6, wherein the memory cells are arranged in columns and rows, wherein the one or more memory cells comprise memory cells positioned in the same row in the array as the selected memory cell.
 8. The method of claim 6, wherein the memory cells are arranged in columns and rows, wherein the one or more memory cells comprise memory cells positioned in the same column in the array as the selected memory cell.
 9. A method of retrieving data from a memory cell, the method comprising: sensing an electrical condition of a first memory cell within an array of memory cells; and determining a logical state for the first memory cell based at least in part on the electrical condition and an electrical condition and/or logical state associated with at least one memory cell of the array adjacent to the first memory cell.
 10. The method of claim 9, wherein determining the logical state comprises performing a Viterbi algorithm on the electrical condition of the first memory cell and the electrical condition and/or logical state associated with the at least one memory cell.
 11. The method of claim 9, wherein each of the memory cells in the array comprises a floating gate transistor, wherein sensing the electrical condition comprises applying a read voltage to the floating gate transistor of the first memory cell, and detecting a current flowing through the floating gate transistor or the threshold voltage value of the floating gate transistor.
 12. An apparatus comprising: an array of memory cells, each of the memory cells being configured to store charges indicative of a data digit; and a sense circuit configured to detect values of the charges stored in selected ones of the memory cells, wherein the apparatus is configured to process the detected values in accordance with a Viterbi algorithm.
 13. The apparatus of claim 12, wherein the memory cells are arranged in columns and rows, wherein the sense circuit is configured to detect the values of charges stored in a selected row of memory cells.
 14. The apparatus of claim 13, wherein each of the memory cells comprises a floating gate transistor including a floating gate, wherein the sense circuit is configured to detect a number of electrons stored in each of the floating gates of the selected row of memory cells.
 15. The apparatus of claim 14, wherein the sense circuit is configured to detect currents flowing through the floating gate transistors or the threshold voltage values of the floating gate transistors.
 16. The apparatus of claim 13, wherein the apparatus is further configured to determine errors associated with paths leading to each possible state of one of the selected memory cells at least partially based on the detected value of charges and inter-signal interference on the selected memory cell; wherein the apparatus is further configured to select one of the paths leading to each possible state at least partially based on an accumulation of the determined errors such that the selected one of the paths has a minimum accumulated error.
 17. The apparatus of claim 16, wherein the apparatus is configured to sequentially repeat determining the errors and selecting one of the paths for each of the selected row of memory cells.
 18. The apparatus of claim 17, wherein the apparatus is further configured to select a state of the last memory cell in the selected row of memory cells at least partially based on errors associated with paths leading to possible states of the last memory cell, wherein the apparatus is further configured to select a state of each of the other memory cells in the selected row of memory cells backward from the selected state of the last memory cell, using the selected paths having a minimum accumulated error, thereby determining the data stored in the selected row of memory cells.
 19. The apparatus of claim 16, wherein the inter-signal interference comprises inter-signal interference from one or more memory cells adjacent to the selected memory cell.
 20. The apparatus of claim 12, wherein the apparatus comprises a flash memory device. 